Fleece's no-show meant they were voted out by the other Scarborough and District League clubs.
The pub side played in the league's third division last season but just missed out on promotion in their maiden season.
Another Whitby side, Fisherlads, quit the league.
The make-up of next season's league will now be decided at an extraordinary general meeting at the Mere Social Club this Monday.
The constitution could not be agreed for the 2008/09 campaign at the AGM, mainly because of problems with the second division having just eight sides.
It was decided to give the relevant teams a week to think about moving up a division before a final decision is made.
Eight new clubs were voted in – Filey Spartans, Seamer Sports Reserves, Eastfield Reserves, Riskers, Castle Tavern, Ryedale, West Pier Reserves and Newlands Reserves.
Last season's bottom two teams, Ayton Reserves and Scalby Reserves, were re-elected.
A decision was also passed which will see the captain of every team wear an armband next season.
This Monday's EGM will start at 7pm.
All clubs are asked to attend.